Question

Question #407aa

Answer 1

`[-3,5]`

Explanation:

Formatted question: `1+2|x-1|<=9`

First we isolate the absolute value by subtracting 1 from both sides then dividing both sides by 2:
`2|x-1|<=8`
`|x-1|<=4`

Since know that `x-1` can be either positive or negative, but its distance from `0` must be less than or equal to `4`, we can remove the absolute value by keeping `x-1` equal to or between `-4` and `4`:
`-4<=x-1<=4`

Now we add `1` to everything to isolate the `x` in the middle:
`-3<=x<=5`

Therefore, our solution for `x` is the interval `[-3,5]`.